Module lm63

The Luz and Meiboom (1963) 2-site fast exchange LM63 model.

Description

This module is for the function, gradient and Hessian of the LM63 model.

References

The model is named after the reference:

• Luz, S. and Meiboom S., (1963) Nuclear Magnetic Resonance study of protolysis of trimethylammonium ion in aqueous solution - order of reaction with respect to solvent, J. Chem. Phys., 39, 366-370 (DOI: 10.1063/1.1734254).

Equations

The equation used is:

                 phi_ex   /     4 * nu_cpmg         /     kex     \ \ 
   R2eff = R20 + ------ * | 1 - -----------  * tanh | ----------- | | ,
                  kex     \         kex             \ 4 * nu_cpmg / /

where:

   phi_ex = pA * pB * delta_omega^2 ,

kex is the chemical exchange rate constant, pA and pB are the populations of states A and B, and delta_omega is the chemical shift difference between the two states.

Links

More information on the LM63 model can be found in the:

• relax wiki,
• relax manual,
• relaxation dispersion page of the relax website.

Functions

r2eff_LM63(r20=None, phi_ex=None, kex=None, cpmg_frqs=None, back_calc=None, num_points=None)
Calculate the R2eff values for the LM63 model.

Variables

__package__ = 'lib.dispersion'

Imports: tanh

Function Details

r2eff_LM63(r20=None, phi_ex=None, kex=None, cpmg_frqs=None, back_calc=None, num_points=None)

Calculate the R2eff values for the LM63 model.

See the module docstring for details.

Parameters:

• r20 (float) - The R20 parameter value (R2 with no exchange).
• phi_ex (float) - The phi_ex parameter value (pA * pB * delta_omega^2).
• kex (float) - The kex parameter value (the exchange rate in rad/s).
• cpmg_frqs (numpy rank-1 float array) - The CPMG nu1 frequencies.
• back_calc (numpy rank-1 float array) - The array for holding the back calculated R2eff values. Each element corresponds to one of the CPMG nu1 frequencies.
• num_points (int) - The number of points on the dispersion curve, equal to the length of the cpmg_frqs and back_calc arguments.